One-loop renormalization group study of boson-fermion mixtures

TL;DR

This paper uses Wilsonian renormalization group analysis to study a weakly interacting boson-fermion mixture, revealing fixed points, decoupling behavior, and potential pairing instability, with implications for emergent supersymmetry.

Contribution

It provides a one-loop RG analysis of boson-fermion mixtures, identifying fixed points and the behavior of interactions, including the decoupling at the Wilson-Fisher fixed point and pairing instability.

Findings

Fermion loop contributions vanish at large scales.

Two fixed points identified: Gaussian and Wilson-Fisher.

Boson-fermion interaction decouples at the Wilson-Fisher fixed point.

Abstract

A weakly interacting boson-fermion mixture model was investigated using Wisonian renormalization group analysis. This model includes one boson-boson interaction term and one boson-fermion interaction term. The scaling dimensions of the two interaction coupling constants were calculated as 2-D at tree level and the Gell-Mann-Low equations were derived at one-loop level. We find that in the Gell-Mann-Low equations the contributions from the fermion loops go to zero as the length scale approaches infinity. After ignoring the fermion loop contributions two fixed points were found in 3 dimensional case. One is the Gaussian fixed point and the other one is Wilson-Fisher fixed point. We find that the boson-fermion interaction decouples at the Wilson-Fisher fixed point. We also observe that under RG transformation the boson-fermion interaction coupling constant runs to negative infinity with a small negative initial value, which indicates a boson-fermion pairing instability. Furthermore, the possibility of emergent supersymmetry in this model was discussed.